Assignments February 9, 2012 due February 10, 2012
6.1.1 (6-7 to 6-11)
Circle Graphs
Data can be found everywhere in the world. When scientists conduct experiments, they collect data. Advertising agencies collect data to learn which products consumers prefer. In Chapter 4 you developed histograms and box-and-whisker plots to represent measures (such as lengths of frog jumps). However, how can you represent data that is non- numerical or that cannot be represented on a number line? Today you will look at a data display that is used for data that comes in categories or groups. As you work, keep these questions in mind:
What portion is represented?
Should I use a fraction or a percent?
Am I measuring in percents or degrees?
February 10, 2012 due February 13, 2012
6.1.2 (6-16 to 6-20)
Organizing Data in a Scatterplot
In previous chapters and Lesson 6.1.1, you have been looking at single data sets, such as world population. Often we need to compare two measurements to answer a question or to see a connection between two types of data. For example, comparing the odometer reading of a car to the price of a car can help determine if these factors are related. In this lesson you will study scatterplots, a new tool for visually presenting data, as a way to relate two sets of measurements. You will be asked to analyze the data to see if you can make predictions or come to any conclusion about the relationships that you find.
As you work with your team today, use these focus questions to help direct your discussion:
How can I organize data?
Can I use this data to make a prediction?
What does a point represent?
Is there a connection between the two factors?
February 13, 2012 due February 14, 2012
6.1.3 (6-27 to 6-31)
Identifying Correlation
When is it reasonable to make a prediction? For example, when you know the height of a tree, can you predict the size of its leaves? Or if you know the outdoor temperature for the day, can you predict the number of glasses of water you will drink during the day?
In Lesson 6.1.2 you found that some data sets were related and others were not. In this lesson you will look at different situations and decide if they show a relationship, and if that relationship allows you to make a prediction. As you work with your team today, use these focus questions to help direct your discussion:
When one value goes up, what happens to the other one?
Is there a relationship between one thing changing and the other changing?
Can I make a prediction?
February 14, 2012 due February 16, 2012
6.1.4 (6-37 to 6-41)
Introduction to Linear Rules
In Lessons 6.1.2 and 6.1.3, you made scatterplots and examined at how data was related. With your team, you will now explore how some kinds of correlations in scatterplots can be used to help make predictions. So far, the data you have graphed has been a collection of points that you have gathered from the world around you. Today we will begin to collect data from a mathematical situation and attempt to use this data to make predictions. This data, when displayed on a graph, will be like a scatterplot in some ways and different in other ways.
February 16, 2012 due February 17, 2012
6.1.5 (6-48 to 6-52)
Intercepts
In past lessons you looked at data from several situations. Sometimes the data appeared to be random and sometimes it had a predictable pattern. When data has a rule-based pattern, we can make predictions by finding other data points that fit the pattern.
February 17, 2012 due January 27, 2012
6.1.6 (6-59 to 6-64)
Tables, Linear Graphs, and Rules
In the previous lesson you made a graph showing how the water level in a tank changed as it was being drained at a constant rate. You noticed that the graph made a straight line. Today you will complete a table and graph what happens as the Giant Pacific Octopus tank is being filled. As you work with your team, think about the following questions:
How is the line changing?
What information can we get from a rule?
When does a graph form a straight line?
When does it not?
February 27, 2012 due January 28, 2012
6.1.extension activity (6-68 to 6-72)
Finding and Describing Relationships
Today you will become a point on a life-size, human graph. Your teacher will give the class instructions for how to form human graphs. Then you will work in study teams to complete the problems below.
February 28, 2012 due March 1, 2012
6.2.1 (6-78 to 6-82)
Solving Equations
In Chapter 5, you figured out how to determine what values of x make one expression greater than another. In this lesson you will study what can be learned about x when two expressions are equal. As you work today, focus on these questions:
What if both sides are equal?
Is there more than one way to simplify?
What value(s) of x will make the expressions equal?
March 1, 2012 due March 2, 2012
6.2.2 (6-88 to 6-92)
Checking Solutions and the Distributive Property
Sometimes a person’s life can depend on the solution of a problem. For example, when skydiving teams jump from airplanes and aim for specific targets on the ground they need to carefully plan their speed and timing. If they are trying to land in a sports stadium as entertainment before a baseball game and they open their parachutes too soon, they may miss the landing area and crash into a building or a tree. If they jump out of the plane too soon, they may run into another skydiver. Even a small miscalculation could be dangerous.
Solving a problem is one challenge. However, once solved, it is important to have ways to know if the solution you found is correct. In this lesson you will be solving equations and finding ways to determine if your solution makes the equation true.
March 2, 2012 due March 5, 2012
6.2.3 (6-99 to 6-103)
Solving Equations and Recording Work
In this lesson, you will continue to improve your skills at simplifying and solving more complex equations. You will develop ways to record your solving strategies so that another student can understand your steps without seeing your Equation Mat. Consider the following questions as you work today.
How can I record the steps I use to solve? How can I record what is on the Equation Mat after each step?
March 5, 2012 due March 6, 2012
6.2.4 (6-108 to 6-112)
Using a Table to Write Equations from Word Problems
In the last few lessons you used algebra tiles and Equation Mats to solve problems where variables represented specific numbers. Those tools are related to the processes you have used to solve word problems where a specific value is unknown. Today you will connect these two tools and the expressions you wrote using a part of the 5-D Process to extend your repertoire for solving problems.
March 6, 2012 due March 8, 2012
6.2.5 (6-114 to 6-118)
Writing and Solving Equations
Engineers investigate practical problems to improve people’s quality of life. To investigate solutions to problems they often build models. These models can take various forms. For example, a structural engineer designing a bridge might build a small replica of the bridge. Civil engineers studying the traffic patterns in a city might create equations that model traffic flows into and out of a city at different times.
In this lesson you will be building equations to model and solve problems based on known information. As you work today keep the following questions in mind:
What does x represent in the equation?
How does the equation show the same information as the problem?
Have I answered the question?
March 8, 2012 due March 9, 2012
6.2.6 (6-124 to 6-128)
Cases With Infinite or No Solutions
Are all equations solvable? Are all solutions a single number? Think about this: Annika was born first and her brother William was born 4 years later. How old will William be when Annika is twice his age? How old will William be when Annika is exactly the same as his age?
In this lesson you will continue to practice your strategies of combining like terms, removing zeros and balancing to simplify and compare two expressions, but you will encounter unusual situations where the solution may be unexpected. As you work today, focus with your team on these questions:
What if both sides are not equal?
Are there many values of x that will make the expressions equal?
Is there always a solution?
March 9, 2012 due March 12, 2012
6.2.7 (6-135 to 6-139)
Choosing a Solving Strategy
The 5-D Process and algebra tiles are useful tools for solving problems. Today you will practice writing equations from word problems and solving them using any of the tools you know. We are developing an efficient set of tools to solve any word problem. Having a variety of methods will allow you to choose the one that makes sense to you and ultimately makes you a more powerful mathematician.
March 12, 2012
Chapter 6 Closure
Reflection and Synthesis
The activities below offer you a chance to reflect on
what you have learned during this chapter. As you
work, look for concepts that you feel very comfortable
with, ideas that you would like to learn more about, and
topics you need more help with. Look for connections
between ideas as well as connections with material you
learned previously.
Assignments January 12, 2012 due January 13, 2012
5.1.1 (5-7 to 5-12)
Inverse Operations
Variables are useful tools to represent an unknown number. In some situations they represent a specific number, and in other situations they represent a collection of possible values. In previous chapters you have used variables to describe patterns in rules, to write lengths in perimeter expressions, and to define unknown quantities in word problems. In this chapter you will continue your work with variables and explore new ways to use them to identify specific values.
As you work in this chapter, you will often be called upon to reverse a process or operation in order to rewrite an expression or relationship. Applying this Way of Thinking by considering how to work in a different direction will help you understand several of the tools you will learn about in this chapter.
January 13, 2012 due January 16, 2012
5.1.2 (5-21 to 5-25)
Translating Situations into Algebraic Expressions
In Lesson 5.1.1, you looked at how mathematical “magic tricks” work by using inverse operations. In this lesson, we will connect the algebra tile picture to another representation of the situation: the variable expression. Consider the following questions today:
How can I visualize it?
How can I write it?
How can I express this situation efficiently?
January 16, 2012 due January 17, 2012
5.1.3 (5-34 to 5-39)
Simplifying Algebraic Expressions
In the previous lesson, you represented more complex mathematical tricks with variable expressions instead of algebra tiles because the expressions were more efficient. In this lesson, you will explore various ways to make expressions simpler by making parts of them zero.
Zero is a relative newcomer to the number system. Its first appearance was as a placeholder around 400 B.C. in Babylon. The Ancient Greeks philosophized about whether zero was even a number: “How can nothing be something?” East Indian mathematicians are generally recognized as the first culture to represent the quantity zero as a numeral and number in its own right about 600 A.D.
Zero now holds an important place in mathematics both as a numeral representing the absence of quantity as well as a placeholder. Did you know there is no year 0 in the Gregorian calendar system (our current calendar system of 365 days in a year)? Until the creation of zero, number systems began at one. Consider the following questions as you work today:
How can I create a zero?
How can I rewrite this expression in the most efficient way?
January 17, 2012 due January 19, 2012
5.2.1 (5-45 to 5-49)
Comparing Expressions
You have been working with writing and simplifying expressions that represent the steps of a number trick. As you wrote these expressions you learned that it was helpful to simplify them by combining like terms and removing zeros. In this lesson you and your teammates will use a tool for comparing expressions to determine if one expression is greater than the other or if they are equal, that is, equivalent ways of writing the same thing.
Remember that to represent expressions with algebra tiles, you will need to be very careful about how positive and negative are distinguished. To help understand the diagrams in the text, the legend showing the shading for +1 and –1 at right will be placed on every page. This model also represents a zero pair.
January 19, 2012 due January 20, 2012
5.2.2 (5-55 to 5-60)
Comparing Quantities with Variables
Have you ever tried to make a decision when the information you have is uncertain? Perhaps you have tried to make plans on a summer day only to learn that it might rain. In that case, your decision might have been based on the weather, such as, “I will go swimming if it doesn’t rain, or stay home and play video games if it does rain.” Sometimes in mathematics solutions might depend on something you do not know, like the value of the variable. Today you will study this kind of situation.
January 20, 2012 due January 23, 2012
5.2.3 (5-67 to 5-71)
One Variable Inequalities
You have used Expression Comparison Mats to compare two expressions and found that sometimes it is possible to determine which expression is greater. You will again compare expressions, this time finding the values for the variable that make one expression greater than the other.
January 23, 2012 due January 24, 2012
5.2.4 (5-78 to 5-82)
Solving One Variable Inequalities
In this lesson, you will work with your team to develop and describe a process for solving linear inequalities. As you work, use the following questions to focus your discussion.
What is a solution?
What do all of the solutions have in common?
What is the greatest solution?
What is the smallest solution?
January 24, 2012 due January 26, 2012
5.3.1 (5-89 to 5-93)
Introduction to Constructions
Architects and drafters make careful drawings before buildings are built. The drawings represent how the building should be constructed. They show the thickness of the walls and where doors, windows, and pipes will be. To make these precise diagrams, professionals often use special computer software. However, some architects prefer to draw the diagrams by hand. They use special drawing tools that look something like those in the drawing at right, including a right triangle tool and a device for measuring angles called a protractor.
Building plans are just one example of a precise geometric drawing. Mathematicians have used these basic tools to draw accurate diagrams for other reasons. The process of constructing, or building, shapes that meet different guidelines can help you understand many of the specific characteristics of those shapes.
In this lesson, you will be introduced to some ideas of mathematical construction and will construct your own shapes. As you work today, use the questions below to start mathematical discussions:
What is the relationship?
How can we describe it?
How do we know for sure?
January 26, 2012 due January 27, 2012
5.3.2 (5-99 to 5-104)
Compass Constructions
A compass is a simple tool that allows circles to be drawn quickly and accurately. Using this simple tool along with a ruler allows one to make precise drawings. In this lesson you will use a compass and ruler to build shapes, construct perpendicular lines, and partition segments.
January 27, 2012 due January 30, 2012
5.3.3 (5-110 to 5-115)
Circumference and Diameter Ratios
The ability to measure objects without standard measuring tools is often very convenient. Have you ever seen anyone estimate the time until the sun sets by extending their arms and seeing how many fists there are from the horizon to the sun? Others use the distance from the tip of their thumb to their knuckle as an approximate inch. Today you will use your own foot as a unit of measure to look at another mathematical relationship.
January 30, 2012 due January 31, 2012
5.3.4 (5-125 to 5-129)
Circle Area
The ratio known as ! (read, “ pi ”) was first discovered by the Babylonians nearly 4000 years ago. Over the years, Egyptian, Chinese, and Greek mathematicians also found the constant ratio between the circumference and diameter of a circle by using measurement. The Greek letter ! has been used to represent this ratio since the 1700s when it was made popular by the Swiss mathematician Euler (pronounced “oy-ler”). Even though this ratio has been known for many years, the value commonly used for ! is still only an approximation.
January 31, 2012
Chapter 5 Closure
Reflection and Synthesis
The activities below offer you a chance to reflect on
what you have learned during this chapter. As you
work, look for concepts that you feel very comfortable
with, ideas that you would like to learn more about, and
topics you need more help with. Look for connections
between ideas as well as connections with material you
learned previously.
November 22, 2011 due November 28, 2011
4.1.1 (4-9 to 4-14)
Part-Whole Relationships
Food labels tell you about what is in the food you eat. The nutrition facts label lists the percentages of vitamins and minerals in each serving. But often it does not tell you exactly how much of each vitamin or mineral is in the food or how much you should have each day to be healthy.
If you know how much Vitamin C is in a serving, can you figure out how much is needed in a day? To help you answer questions like that, this section will develop strategies that will help you find information about parts and wholes.
November 28, 2011 due November 29, 2011
4.1.2 (4-19 to 4-23)
Finding and Using Percentages
How are sales advertised in different stores? In a clothing store, items are often marked with signs saying, “20% off” or “40% discount.” In a grocery store, sale items are usually listed by price. For example, pasta is marked, “Sale price 50¢,” or boxes of cereal are marked “$2.33 each.” In the clothing store you are able to see how much the discount is, but the price you will pay is often not stated. On the other hand, sometimes in the grocery story it is not possible to tell the size of the discount. It might only be a small fraction of the original price.
The actual dollar amount of the discount and the percentage comparing it to the whole are important information that help you decide if you are getting a good deal. Today you will create complete information about a sale situation from the information given in a problem.
By the end of this lesson, you will be expected to answer the following target questions:
How can I find a percentage of a whole?
How can I find a percent if you have two parts that make a whole?
How can I find the whole amount if you know the parts?
November 29, 2011 due December 1, 2011
4.2.1 (4-30 to 4-34)
Measures of Central Tendency
You are exposed to a huge amount of information every day in school, in the news, in advertising, and in other places. It helps to have tools to be able to understand what different data mean. In this section, you will turn your attention to what you can learn (and not learn) from data.
December 1, 2011 due December 2, 2011
4.2.2 (4-40 to 4-48)
Multiple Representations of Data
Mark Twain, a famous American writer and humorist (1835–1910), once said, “Get your facts first, and then you can distort them as much as you please. (Facts are stubborn, but statistics are more pliable.)” What do you think he meant? Much of what we learn and interpret about different sets of data is based on how it is presented.
In this lesson you will use several mathematical tools to look at data in different ways. As you work, use these questions to help focus your discussions with your team:
What can we conclude based on this representation?
What cannot be concluded based on this representation?
How are the representations related?
December 2, 2011 due December 5, 2011
4.2.3 (4-56 to 4-60)
Analyzing Box-and-Whisker Plots
So far in this course, you have considered static (unchanging) sets of data, such as temperatures on a specific date in time or the lengths of leaps of the top performing frog jumpers. However, most of the time, data sets are growing and changing. For example, as you take quizzes or tests in your class, your overall average changes. Similarly, if you decided to track the average temperature on November 1 for each year, then the average you calculate each year would change as you add new pieces of data.
Today, you will explore how each representation changes when the data it describes changes. You will investigate questions like, “What happens if a new piece of data is added?” and “Is there a way to add data without changing the representation?” You can help your study team succeed today by sharing your ideas and your reasoning out loud in your team and by working hard to understand other people’s ideas.
December 5, 2011 due December 6, 2011
4.2.4 (4-65 to 4-68)
Comparing and Choosing Representations
There are many different representations for displaying data. In this chapter, you have looked at three different representations: histograms, stem-and-leaf plots, and box-and-whisker plots. Today you will compare these representations to decide when one might be a better way to communicate information from a set of data.
December 6, 2011 due December 8, 2011
4.3.1 (4-75 to 4-79)
Dilations and Similar Figures
Have you ever wondered how different mirrors work? Most mirrors show you a reflection that looks just like you. But other mirrors, like those commonly found at carnivals and amusement parks, reflect back a face that is stretched or squished. You may look taller, shorter, fatter or skinnier. These effects can be created on the computer if you put a picture into a photo program. If you do not follow the mathematical principles of proportionality when you enlarge or shrink a photo, you may find that the picture is stretched thin or spread out, and not at all like the original. Today you will look at enlarging and reducing shapes using dilations to explore why a shape changes in certain ways.
December 8, 2011 due December 9, 2011
4.3.2 (4-86 to 4-90)
Identifying Similar Shapes
Have you ever noticed how many different kinds of cell phones there are? Sometimes you might have a cell phone that is similar to one of your friends’ cell phones because it is the same brand, but it might be a different model or color. Occasionally, two people will have the exact same cell phone, including brand, model and color. Sorting objects into groups based on their sameness is also done in math. As you work with your team to sort shapes, ask the following questions:
How do the shapes grow or shrink?
What parts can we compare?
How can we write the comparison?
December 9, 2011 due December 12, 2011
4.3.3 (4-98 to 4-102)
Working With Corresponding Sides
Sometimes graphic artists have a shape that they need to make larger to use for a sign or make smaller to use for a bumper sticker. They have to be sure that the shapes look the same no matter what size they are. How do artists know what the side length of a similar shape should be, if it needs to be larger or smaller than the original?
December 12, 2011 due December 13, 2011
4.3.3 (4-108 to 4-112)
Solving Problems Involving Similar Shapes
Architects create scaled plans for building houses, artists use sketches to plan murals for the sides of buildings, and companies create smaller sizes of their products for display in stores. Each of these models is created to show all of the information about the “real” object, without being the actual size of the object. Today you will work with your team to find strategies that you can use when you are missing some of the information about a set of similar shapes. As you work, look for more than one way to solve the problem.
December 13, 2011
Chapter 3 Closure
Reflection and Synthesis
The activities below offer you a chance to reflect on
what you have learned during this chapter. As you
work, look for concepts that you feel very comfortable
with, ideas that you would like to learn more about, and
topics you need more help with. Look for connections
between ideas as well as connections with material you
learned previously.
Test October 28, 2011
November 21, 2011 December 14, 2011
Assignments
October 31, 2011 due November 1, 2011
3.1.1 (3-7 to 3-11)
Area of Rectangular Shapes
Mathematics can be used to describe patterns in the world. Scientists use math to describe various aspects of life, including how cells multiply, how objects move through space, and how chemicals react. Often, when scientists try to describe these patterns, they need to describe something that changes or varies. Scientists call those quantities that change variables, and represent them using letters and symbols.
In this course you will spend time learning about variables, what they can represent, and how they can serve different purposes. To start, you will use variables to describe the dimensions and area of different shapes and begin to organize those descriptions into algebraic expressions.
As you work with your teammates, use the following questions to help focus your team’s discussion:
How can we organize groups of things?
What is the area?
Which lengths can vary?
November 1, 2011 due November 3, 2011
3.1.2 (3-18 to 3-23)
Naming Perimeters of Algebra Tiles
How much homework do you have each night? Some nights you may have a lot, while other nights you may have no homework at all. The amount of homework you have varies from day to day. In mathematics we use letters such as x and y, called variables, to represent quantities that are not constant.
In Lesson 3.1.1 you used variables to name lengths that could not be precisely measured. Using variables allows you to work with lengths that you do not know exactly. Today you will work with your team to write expressions to represent the perimeters of different shapes using variables. As you work with your teammates, use the following questions to help focus your team’s discussion:
Which lengths can vary?
How can we see the perimeter?
How can we organize groups of things?
November 1, 2011 due November 3, 2011
3.1.1 (3-7 to 3-11)
Area of Rectangular Shapes
Mathematics can be used to describe patterns in the world. Scientists use math to describe
various aspects of life, including how cells multiply, how objects move through space, and
how chemicals react. Often, when scientists try to describe these patterns, they need to
describe something that changes or varies. Scientists call those quantities that change
variables, and represent them using letters and symbols.
In this course you will spend time learning about variables, what they can represent, and
how they can serve different purposes. To start, you will use variables to describe the
dimensions and area of different shapes and begin to organize those descriptions into
algebraic expressions.
As you work with your teammates, use the following questions to help focus your team’s
discussion:
How can we organize groups of things?
What is the area?
Which lengths can vary?
November 3, 2011 due November 4, 2011
3.1.2 (3-18 to 3-23)
Naming Perimeters of Algebra Tiles
How much homework do you have each night? Some nights you may have a lot, while
other nights you may have no homework at all. The amount of homework you have varies
from day to day. In mathematics we use letters such as x and y, called variables, to
represent quantities that are not constant.
In Lesson 3.1.1 you used variables to name lengths that could not be precisely measured.
Using variables allows you to work with lengths that you do not know exactly. Today you
will work with your team to write expressions to represent the perimeters of different
shapes using variables. As you work with your teammates, use the following questions to
help focus your team’s discussion:
Which lengths can vary?
How can we see the perimeter?
How can we organize groups of things?
November 4, 2011 due November 7, 2011
3.1.3 (3-29 to 3-33)
Combining Like Terms
In Lesson 3.1.2, you looked at different ways the perimeter of algebra tiles can be written,
and created different expressions to describe the same perimeter. Expressions that
represent the same perimeter in different ways are called equivalent. Today, you will
extend your work with writing and rewriting perimeters to more complex shapes. You
will rewrite expressions to determine whether two perimeters are equivalent or different.
As you work today, keep these questions in mind:
Are there like terms I can combine?
How can I rearrange it?
How can I see (visualize) it?
November 7, 2011 due November 8, 2011
3.1.4 (3-38 to 3-42)
Evaluating Variable Expressions
In the past three lessons, you have learned how to find the perimeter and area of a shape
using algebra tiles. Today, you will challenge the class to find the perimeter and area of
shapes that you create. As you work, keep in mind these questions:
Which lengths are constant?
Which lengths can change?
November 8, 2011 due November 10, 2011
3.1.5 (3-49 to 3-53)
Perimeter and Area of Algebra Tile Shapes
People often assume that area and perimeter are related. It seems reasonable that if the
area of a shape gets bigger (or smaller), then its perimeter should also get bigger (or
smaller). But is this always true? In Chapter 1 you learned that the “tiles” could stay the
same, but you could increase the “toothpicks” by changing the arrangement of squares. In
this lesson you will continue to investigate whether there is a relationship between
perimeter and area using algebra tiles.
As you work with your team, it is important that you share your ideas so that you are able
to understand many different ways of seeing the shapes. Be prepared to justify how you
are finding perimeters and how you are simplifying the expressions. Ask yourself these
questions to help you to explain your reasoning:
How can I see the perimeter?
Where am I adding (or covering) length?
How can I rearrange the tiles?
November 10, 2011 due November 11, 2011
3.2.1 (3-60 to 3-64)
Describing Relationships Between Quantities
You may not know it, but you use mathematical thinking every day. You think
mathematically when you figure out if you can afford items you want to buy, or when you
read a graph on a web page. You also think mathematically when you double a recipe or
when you estimate how much longer it will take to get somewhere based on how far you
still have to go. Math can describe many of the relationships in the world around you.
Building your interpretation skills and developing ways to represent situations will help
you solve problems. In this section you will learn new ways to show your thinking when
using math to solve problems. As you work today, think about the following questions:
How can I represent this with a diagram?
Who has more? Who has less?
November 11, 2011 due November 14, 2011
3.2.2 (3-71 to 3-75)
Solving a Word Problem
You have seen that being able to draw diagrams and describe relationships is helpful for
solving problems. In this lesson, you will learn another way to organize your thinking as
you solve word problems.
November 14, 2011 due November 15, 2011
3.2.3 (3-84 to 3-88)
Strategies for Using the 5-D Process
Math is used to solve challenging problems that apply to daily life. For example, how
much fresh water is on the planet? How many area codes (for telephone numbers) are
needed in a city? Where should a city build transportation lines such as city bus systems
and subways to reduce traffic on the freeways? Mathematics can provide helpful insights
for the solutions.
When trying to solve a new and challenging problem, it is useful to have a strategy. The
5-D Process that you learned about in Lesson 3.2.2 will often work when you are trying to
solve a problem you have not seen before.
In this lesson you will practice using this process to solve more word problems and you
will compare the different ways that your classmates use the 5-D Process to help them.
Be sure to write your work neatly and be prepared to justify your reasoning.
As you work using the 5-D Process, consider the following questions:
How can we describe the problem?
How can we decide how to label the columns?
How can we organize the columns?
How can we decide which quantity to start with?
Does it matter which one we choose?
How can we decide which number to try first?
November 15, 2011 due November 17, 2011
3.2.4 (3-99 to 3-103)
Using Variables to Represent Quantities in Word Problems
In Section 2.1, you used variables to help you describe the perimeter of tiles. In that
situation x could be stretched to represent any positive number. Today you will continue
to use the 5-D Process as you solve word problems and you will use a variable to represent
the unknown value in the problem.
Think of these questions as you work on the problems today:
What is the problem asking?
What is the relationship between the quantities involved?
How can I choose which part of the problem to represent with a variable?
November 17, 2011 due November 18, 2011
3.2.5 (3-105 to 3-108)
More Word Problem Solving
So far in Section 3.2, you have been using a 5-D Process as a way to organize and solve
problems. Today you will continue using this process to solve problems in a variety of
situations.
As you work, use the following questions to focus your team’s discussion:
What is the problem asking?
What is the relationship between the quantities involved?
How can we decide which part of the problem to represent as x ?
What if a different quantity were represented with x?
November 18, 2011
Chapter 3 Closure
Reflection and Synthesis
The activities below offer you a chance to reflect on
what you have learned during this chapter. As you
work, look for concepts that you feel very comfortable
with, ideas that you would like to learn more about, and
topics you need more help with. Look for connections
between ideas as well as connections with material you
learned previously.
October 7, 2011 due October 17, 2011
2.2.4 extension activity (2-85 to 2-89)
Using Rigid Transformations
In the last several lessons you have described translations using coordinates, and developed strategies for determining where an object started when you know how it was translated and its final position. In this lesson, you will continue to practice transforming objects on a coordinate grid by translating (sliding), rotating (turning), and reflecting (flipping). As you work, visualize what each object will look like after the transformation and use the graph to check your prediction.
October 17, 2011 due October 18, 2011
2.3.1 (2-97 to 2-101)
Multiplication of Fractions
You often only need part of something. You might need part of a gallon of gasoline to fill the tank of a scooter, part of a can of paint to finish covering a wall, or part of a piece of paper to complete an assignment.
But what happens when you need a part of a part? Cooks, construction workers, and city planners often need to find part of something that is already a part of something else.
As you work with your team to find parts of parts, be sure to draw diagrams and clearly label all of the pieces in them so that you know what they represent. Think about the following questions:
How can I represent it?
What does each part represent in the situation?
October 18, 2011 due October 20, 2011
2.3.2 (2-77 to 2-81)
Decomposing and Recomposing Area
In previous classes you have had experience with finding the area of squares and other rectangles, but what about finding the area of irregular shapes? Landscape designers, floor tilers, and others often have to deal with areas that are made of several shapes combined into one. As you work on the problems in this lesson, you will need to visualize the new shapes, and predict what they will look like after they are changed.
As you work through this section, it will be important to describe how you see different shapes and to organize your work to show your thinking. Ask each other these questions to get discussions started in your study team:
What other shapes can we see in this figure?
Where should we break this shape apart?
How should we rearrange the pieces?
Will the area change?
October 20, 2011 due October 21, 2011
2.3.3 (2-116 to 2-120)
Area of Parallelograms
In Lesson 2.3.2, you worked with your study team to rearrange two irregular shapes into rectangles in order to find their areas more easily. Today you will use a technology tool (available at www.cpm.org/students/technology) to investigate the question: Can all shapes be rearranged to make rectangles? As you work, visualize what each shape will look like cut into pieces and how those pieces could fit back together to make a rectangle. Ask yourself these questions while you investigate:
How can I break this shape apart?
How can I rearrange the pieces of the shape to make a new shape?
October 21, 2011 due October 24, 2011
2.3.4 (2-127 to 2-132)
Area of Triangles
So far in this chapter you found the area of different shapes by dividing them into smaller pieces and then putting the pieces back together to make rectangles. In this lesson you will look at strategies for making shapes larger in order to find their areas. As you work today, consider these questions:
How can I make a rectangle?
How are the areas related?
Which lengths help me find the area?
October 24, 2011 due October 25, 2011
2.3.5 (2-137 to 2-141)
Area of Trapezoids
In this chapter, you have used the process of cutting apart and rearranging shapes to help you find their areas. You have also made some shapes larger to help find their area. In this chapter you have developed several different strategies for finding the area of shapes. For example, you have found the sum of the areas of multiple smaller parts, rearranged smaller parts into rectangles to find area, and made shapes bigger in order to find their area. In this lesson you will focus on how to choose a strategy to find the area of a new shape: a trapezoid. As you work with your team, practice visualizing how each shape can be changed or rearranged. Ask each other these questions:
What strategy should we choose?
Which lengths are important?
October 25, 2011 due October 27, 2011
2.3.6 (2-151 to 2-155)
Order of Operations
If you know the length of the base and height of a triangle, how do you find its area? Some people reason this way: Since I know that two of the triangles can make a parallelogram, then the area of the triangle must be half the area of the parallelogram. Therefore, it is half the product of the length of the base and the length of the height.
However, this relationship can also be written as a rule, such as A = 1/2 bh, where A represents the area of theh triangle, b represents the length of the base, and h represents the height of the triangle.
There are many other relationships that can be written with symbols that you may have seen before. Perhaps one of the most famous rules is Einstein’s formula E = mc2 , relating energy, mass, and the speed of light. Work with your team to use some rules you already know to find a quantity.
October 27, 2011 Chapter 2 Closure - Answers are in the packet. Be ready for the test tomorrow.
Quarter 1 Assignments October 3, 2011 due October 6, 2011
2.2.4 (2-77 to 2-81)
Multiplication and Dilation
When an object is translated, rotated or reflected, it stays the same size and shape even though it moves. For this reason, they are called rigid transformations. In this lesson you will explore a new transformation that changes how the object looks. As you work today, ask these questions in your team:
What parts of the shape are changing?
What parts stay the same?
What happens when we multiply by a negative number?
October 4, 2011
ISA testing. No class.
October 7, 2011 due October 17, 2011
2.2.4 extension activity (2-85 to 2-89)
Using Rigid Transformations
In the last several lessons you have described translations using coordinates, and developed strategies for determining where an object started when you know how it was translated and its final position. In this lesson, you will continue to practice transforming objects on a coordinate grid by translating (sliding), rotating (turning), and reflecting (flipping). As you work, visualize what each object will look like after the transformation and use the graph to check your prediction.
October 10-14
Break
October 17, 2011 due October 18, 2011
2.3.1 (2-97 to 2-101)
Multiplication of Fractions
You often only need part of something. You might need part of a gallon of gasoline to fill the tank of a scooter, part of a can of paint to finish covering a wall, or part of a piece of paper to complete an assignment.
But what happens when you need a part of a part? Cooks, construction workers, and city planners often need to find part of something that is already a part of something else.
As you work with your team to find parts of parts, be sure to draw diagrams and clearly label all of the pieces in them so that you know what they represent. Think about the following questions:
How can I represent it?
What does each part represent in the situation?
Grade 7Foundations of Algebra
Quarter 3
Assignments
February 9, 2012 due February 10, 2012
6.1.1 (6-7 to 6-11)
Circle Graphs
Data can be found everywhere in the world. When scientists conduct experiments, they collect data. Advertising agencies collect data to learn which products consumers prefer. In Chapter 4 you developed histograms and box-and-whisker plots to represent measures (such as lengths of frog jumps). However, how can you represent data that is non- numerical or that cannot be represented on a number line? Today you will look at a data display that is used for data that comes in categories or groups. As you work, keep these questions in mind:
What portion is represented?
Should I use a fraction or a percent?
Am I measuring in percents or degrees?
February 10, 2012 due February 13, 2012
6.1.2 (6-16 to 6-20)
Organizing Data in a Scatterplot
In previous chapters and Lesson 6.1.1, you have been looking at single data sets, such as world population. Often we need to compare two measurements to answer a question or to see a connection between two types of data. For example, comparing the odometer reading of a car to the price of a car can help determine if these factors are related. In this lesson you will study scatterplots, a new tool for visually presenting data, as a way to relate two sets of measurements. You will be asked to analyze the data to see if you can make predictions or come to any conclusion about the relationships that you find.
As you work with your team today, use these focus questions to help direct your discussion:
How can I organize data?
Can I use this data to make a prediction?
What does a point represent?
Is there a connection between the two factors?
February 13, 2012 due February 14, 2012
6.1.3 (6-27 to 6-31)
Identifying Correlation
When is it reasonable to make a prediction? For example, when you know the height of a tree, can you predict the size of its leaves? Or if you know the outdoor temperature for the day, can you predict the number of glasses of water you will drink during the day?
In Lesson 6.1.2 you found that some data sets were related and others were not. In this lesson you will look at different situations and decide if they show a relationship, and if that relationship allows you to make a prediction. As you work with your team today, use these focus questions to help direct your discussion:
When one value goes up, what happens to the other one?
Is there a relationship between one thing changing and the other changing?
Can I make a prediction?
February 14, 2012 due February 16, 2012
6.1.4 (6-37 to 6-41)
Introduction to Linear Rules
In Lessons 6.1.2 and 6.1.3, you made scatterplots and examined at how data was related. With your team, you will now explore how some kinds of correlations in scatterplots can be used to help make predictions. So far, the data you have graphed has been a collection of points that you have gathered from the world around you. Today we will begin to collect data from a mathematical situation and attempt to use this data to make predictions. This data, when displayed on a graph, will be like a scatterplot in some ways and different in other ways.
February 16, 2012 due February 17, 2012
6.1.5 (6-48 to 6-52)
Intercepts
In past lessons you looked at data from several situations. Sometimes the data appeared to be random and sometimes it had a predictable pattern. When data has a rule-based pattern, we can make predictions by finding other data points that fit the pattern.
February 17, 2012 due January 27, 2012
6.1.6 (6-59 to 6-64)
Tables, Linear Graphs, and Rules
In the previous lesson you made a graph showing how the water level in a tank changed as it was being drained at a constant rate. You noticed that the graph made a straight line. Today you will complete a table and graph what happens as the Giant Pacific Octopus tank is being filled. As you work with your team, think about the following questions:
How is the line changing?
What information can we get from a rule?
When does a graph form a straight line?
When does it not?
February 27, 2012 due January 28, 2012
6.1.extension activity (6-68 to 6-72)
Finding and Describing Relationships
Today you will become a point on a life-size, human graph. Your teacher will give the class instructions for how to form human graphs. Then you will work in study teams to complete the problems below.
February 28, 2012 due March 1, 2012
6.2.1 (6-78 to 6-82)
Solving Equations
In Chapter 5, you figured out how to determine what values of x make one expression greater than another. In this lesson you will study what can be learned about x when two expressions are equal. As you work today, focus on these questions:
What if both sides are equal?
Is there more than one way to simplify?
What value(s) of x will make the expressions equal?
March 1, 2012 due March 2, 2012
6.2.2 (6-88 to 6-92)
Checking Solutions and the Distributive Property
Sometimes a person’s life can depend on the solution of a problem. For example, when skydiving teams jump from airplanes and aim for specific targets on the ground they need to carefully plan their speed and timing. If they are trying to land in a sports stadium as entertainment before a baseball game and they open their parachutes too soon, they may miss the landing area and crash into a building or a tree. If they jump out of the plane too soon, they may run into another skydiver. Even a small miscalculation could be dangerous.
Solving a problem is one challenge. However, once solved, it is important to have ways to know if the solution you found is correct. In this lesson you will be solving equations and finding ways to determine if your solution makes the equation true.
March 2, 2012 due March 5, 2012
6.2.3 (6-99 to 6-103)
Solving Equations and Recording Work
In this lesson, you will continue to improve your skills at simplifying and solving more complex equations. You will develop ways to record your solving strategies so that another student can understand your steps without seeing your Equation Mat. Consider the following questions as you work today.
How can I record the steps I use to solve? How can I record what is on the Equation Mat after each step?
March 5, 2012 due March 6, 2012
6.2.4 (6-108 to 6-112)
Using a Table to Write Equations from Word Problems
In the last few lessons you used algebra tiles and Equation Mats to solve problems where variables represented specific numbers. Those tools are related to the processes you have used to solve word problems where a specific value is unknown. Today you will connect these two tools and the expressions you wrote using a part of the 5-D Process to extend your repertoire for solving problems.
March 6, 2012 due March 8, 2012
6.2.5 (6-114 to 6-118)
Writing and Solving Equations
Engineers investigate practical problems to improve people’s quality of life. To investigate solutions to problems they often build models. These models can take various forms. For example, a structural engineer designing a bridge might build a small replica of the bridge. Civil engineers studying the traffic patterns in a city might create equations that model traffic flows into and out of a city at different times.
In this lesson you will be building equations to model and solve problems based on known information. As you work today keep the following questions in mind:
What does x represent in the equation?
How does the equation show the same information as the problem?
Have I answered the question?
March 8, 2012 due March 9, 2012
6.2.6 (6-124 to 6-128)
Cases With Infinite or No Solutions
Are all equations solvable? Are all solutions a single number? Think about this: Annika was born first and her brother William was born 4 years later. How old will William be when Annika is twice his age? How old will William be when Annika is exactly the same as his age?
In this lesson you will continue to practice your strategies of combining like terms, removing zeros and balancing to simplify and compare two expressions, but you will encounter unusual situations where the solution may be unexpected. As you work today, focus with your team on these questions:
What if both sides are not equal?
Are there many values of x that will make the expressions equal?
Is there always a solution?
March 9, 2012 due March 12, 2012
6.2.7 (6-135 to 6-139)
Choosing a Solving Strategy
The 5-D Process and algebra tiles are useful tools for solving problems. Today you will practice writing equations from word problems and solving them using any of the tools you know. We are developing an efficient set of tools to solve any word problem. Having a variety of methods will allow you to choose the one that makes sense to you and ultimately makes you a more powerful mathematician.
March 12, 2012
Chapter 6 Closure
Reflection and Synthesis
The activities below offer you a chance to reflect on
what you have learned during this chapter. As you
work, look for concepts that you feel very comfortable
with, ideas that you would like to learn more about, and
topics you need more help with. Look for connections
between ideas as well as connections with material you
learned previously.
Test
March 13, 2012
Assignments
January 12, 2012 due January 13, 2012
5.1.1 (5-7 to 5-12)
Inverse Operations
Variables are useful tools to represent an unknown number. In some situations they represent a specific number, and in other situations they represent a collection of possible values. In previous chapters you have used variables to describe patterns in rules, to write lengths in perimeter expressions, and to define unknown quantities in word problems. In this chapter you will continue your work with variables and explore new ways to use them to identify specific values.
As you work in this chapter, you will often be called upon to reverse a process or operation in order to rewrite an expression or relationship. Applying this Way of Thinking by considering how to work in a different direction will help you understand several of the tools you will learn about in this chapter.
January 13, 2012 due January 16, 2012
5.1.2 (5-21 to 5-25)
Translating Situations into Algebraic Expressions
In Lesson 5.1.1, you looked at how mathematical “magic tricks” work by using inverse operations. In this lesson, we will connect the algebra tile picture to another representation of the situation: the variable expression. Consider the following questions today:
How can I visualize it?
How can I write it?
How can I express this situation efficiently?
January 16, 2012 due January 17, 2012
5.1.3 (5-34 to 5-39)
Simplifying Algebraic Expressions
In the previous lesson, you represented more complex mathematical tricks with variable expressions instead of algebra tiles because the expressions were more efficient. In this lesson, you will explore various ways to make expressions simpler by making parts of them zero.
Zero is a relative newcomer to the number system. Its first appearance was as a placeholder around 400 B.C. in Babylon. The Ancient Greeks philosophized about whether zero was even a number: “How can nothing be something?” East Indian mathematicians are generally recognized as the first culture to represent the quantity zero as a numeral and number in its own right about 600 A.D.
Zero now holds an important place in mathematics both as a numeral representing the absence of quantity as well as a placeholder. Did you know there is no year 0 in the Gregorian calendar system (our current calendar system of 365 days in a year)? Until the creation of zero, number systems began at one. Consider the following questions as you work today:
How can I create a zero?
How can I rewrite this expression in the most efficient way?
January 17, 2012 due January 19, 2012
5.2.1 (5-45 to 5-49)
Comparing Expressions
You have been working with writing and simplifying expressions that represent the steps of a number trick. As you wrote these expressions you learned that it was helpful to simplify them by combining like terms and removing zeros. In this lesson you and your teammates will use a tool for comparing expressions to determine if one expression is greater than the other or if they are equal, that is, equivalent ways of writing the same thing.
Remember that to represent expressions with algebra tiles, you will need to be very careful about how positive and negative are distinguished. To help understand the diagrams in the text, the legend showing the shading for +1 and –1 at right will be placed on every page. This model also represents a zero pair.
January 19, 2012 due January 20, 2012
5.2.2 (5-55 to 5-60)
Comparing Quantities with Variables
Have you ever tried to make a decision when the information you have is uncertain? Perhaps you have tried to make plans on a summer day only to learn that it might rain. In that case, your decision might have been based on the weather, such as, “I will go swimming if it doesn’t rain, or stay home and play video games if it does rain.” Sometimes in mathematics solutions might depend on something you do not know, like the value of the variable. Today you will study this kind of situation.
January 20, 2012 due January 23, 2012
5.2.3 (5-67 to 5-71)
One Variable Inequalities
You have used Expression Comparison Mats to compare two expressions and found that sometimes it is possible to determine which expression is greater. You will again compare expressions, this time finding the values for the variable that make one expression greater than the other.
January 23, 2012 due January 24, 2012
5.2.4 (5-78 to 5-82)
Solving One Variable Inequalities
In this lesson, you will work with your team to develop and describe a process for solving linear inequalities. As you work, use the following questions to focus your discussion.
What is a solution?
What do all of the solutions have in common?
What is the greatest solution?
What is the smallest solution?
January 24, 2012 due January 26, 2012
5.3.1 (5-89 to 5-93)
Introduction to Constructions
Architects and drafters make careful drawings before buildings are built. The drawings represent how the building should be constructed. They show the thickness of the walls and where doors, windows, and pipes will be. To make these precise diagrams, professionals often use special computer software. However, some architects prefer to draw the diagrams by hand. They use special drawing tools that look something like those in the drawing at right, including a right triangle tool and a device for measuring angles called a protractor.
Building plans are just one example of a precise geometric drawing. Mathematicians have used these basic tools to draw accurate diagrams for other reasons. The process of constructing, or building, shapes that meet different guidelines can help you understand many of the specific characteristics of those shapes.
In this lesson, you will be introduced to some ideas of mathematical construction and will construct your own shapes. As you work today, use the questions below to start mathematical discussions:
What is the relationship?
How can we describe it?
How do we know for sure?
January 26, 2012 due January 27, 2012
5.3.2 (5-99 to 5-104)
Compass Constructions
A compass is a simple tool that allows circles to be drawn quickly and accurately. Using this simple tool along with a ruler allows one to make precise drawings. In this lesson you will use a compass and ruler to build shapes, construct perpendicular lines, and partition segments.
January 27, 2012 due January 30, 2012
5.3.3 (5-110 to 5-115)
Circumference and Diameter Ratios
The ability to measure objects without standard measuring tools is often very convenient. Have you ever seen anyone estimate the time until the sun sets by extending their arms and seeing how many fists there are from the horizon to the sun? Others use the distance from the tip of their thumb to their knuckle as an approximate inch. Today you will use your own foot as a unit of measure to look at another mathematical relationship.
January 30, 2012 due January 31, 2012
5.3.4 (5-125 to 5-129)
Circle Area
The ratio known as ! (read, “ pi ”) was first discovered by the Babylonians nearly 4000 years ago. Over the years, Egyptian, Chinese, and Greek mathematicians also found the constant ratio between the circumference and diameter of a circle by using measurement. The Greek letter ! has been used to represent this ratio since the 1700s when it was made popular by the Swiss mathematician Euler (pronounced “oy-ler”). Even though this ratio has been known for many years, the value commonly used for ! is still only an approximation.
January 31, 2012
Chapter 5 Closure
Reflection and Synthesis
The activities below offer you a chance to reflect on
what you have learned during this chapter. As you
work, look for concepts that you feel very comfortable
with, ideas that you would like to learn more about, and
topics you need more help with. Look for connections
between ideas as well as connections with material you
learned previously.
Test
February 2, 2012
Quarter 2
Assignments
November 22, 2011 due November 28, 2011
4.1.1 (4-9 to 4-14)
Part-Whole Relationships
Food labels tell you about what is in the food you eat. The nutrition facts label lists the percentages of vitamins and minerals in each serving. But often it does not tell you exactly how much of each vitamin or mineral is in the food or how much you should have each day to be healthy.
If you know how much Vitamin C is in a serving, can you figure out how much is needed in a day? To help you answer questions like that, this section will develop strategies that will help you find information about parts and wholes.
November 28, 2011 due November 29, 2011
4.1.2 (4-19 to 4-23)
Finding and Using Percentages
How are sales advertised in different stores? In a clothing store, items are often marked with signs saying, “20% off” or “40% discount.” In a grocery store, sale items are usually listed by price. For example, pasta is marked, “Sale price 50¢,” or boxes of cereal are marked “$2.33 each.” In the clothing store you are able to see how much the discount is, but the price you will pay is often not stated. On the other hand, sometimes in the grocery story it is not possible to tell the size of the discount. It might only be a small fraction of the original price.
The actual dollar amount of the discount and the percentage comparing it to the whole are important information that help you decide if you are getting a good deal. Today you will create complete information about a sale situation from the information given in a problem.
By the end of this lesson, you will be expected to answer the following target questions:
How can I find a percentage of a whole?
How can I find a percent if you have two parts that make a whole?
How can I find the whole amount if you know the parts?
November 29, 2011 due December 1, 2011
4.2.1 (4-30 to 4-34)
Measures of Central Tendency
You are exposed to a huge amount of information every day in school, in the news, in advertising, and in other places. It helps to have tools to be able to understand what different data mean. In this section, you will turn your attention to what you can learn (and not learn) from data.
December 1, 2011 due December 2, 2011
4.2.2 (4-40 to 4-48)
Multiple Representations of Data
Mark Twain, a famous American writer and humorist (1835–1910), once said, “Get your facts first, and then you can distort them as much as you please. (Facts are stubborn, but statistics are more pliable.)” What do you think he meant? Much of what we learn and interpret about different sets of data is based on how it is presented.
In this lesson you will use several mathematical tools to look at data in different ways. As you work, use these questions to help focus your discussions with your team:
What can we conclude based on this representation?
What cannot be concluded based on this representation?
How are the representations related?
December 2, 2011 due December 5, 2011
4.2.3 (4-56 to 4-60)
Analyzing Box-and-Whisker Plots
So far in this course, you have considered static (unchanging) sets of data, such as temperatures on a specific date in time or the lengths of leaps of the top performing frog jumpers. However, most of the time, data sets are growing and changing. For example, as you take quizzes or tests in your class, your overall average changes. Similarly, if you decided to track the average temperature on November 1 for each year, then the average you calculate each year would change as you add new pieces of data.
Today, you will explore how each representation changes when the data it describes changes. You will investigate questions like, “What happens if a new piece of data is added?” and “Is there a way to add data without changing the representation?” You can help your study team succeed today by sharing your ideas and your reasoning out loud in your team and by working hard to understand other people’s ideas.
December 5, 2011 due December 6, 2011
4.2.4 (4-65 to 4-68)
Comparing and Choosing Representations
There are many different representations for displaying data. In this chapter, you have looked at three different representations: histograms, stem-and-leaf plots, and box-and-whisker plots. Today you will compare these representations to decide when one might be a better way to communicate information from a set of data.
December 6, 2011 due December 8, 2011
4.3.1 (4-75 to 4-79)
Dilations and Similar Figures
Have you ever wondered how different mirrors work? Most mirrors show you a reflection that looks just like you. But other mirrors, like those commonly found at carnivals and amusement parks, reflect back a face that is stretched or squished. You may look taller, shorter, fatter or skinnier. These effects can be created on the computer if you put a picture into a photo program. If you do not follow the mathematical principles of proportionality when you enlarge or shrink a photo, you may find that the picture is stretched thin or spread out, and not at all like the original. Today you will look at enlarging and reducing shapes using dilations to explore why a shape changes in certain ways.
December 8, 2011 due December 9, 2011
4.3.2 (4-86 to 4-90)
Identifying Similar Shapes
Have you ever noticed how many different kinds of cell phones there are? Sometimes you might have a cell phone that is similar to one of your friends’ cell phones because it is the same brand, but it might be a different model or color. Occasionally, two people will have the exact same cell phone, including brand, model and color. Sorting objects into groups based on their sameness is also done in math. As you work with your team to sort shapes, ask the following questions:
How do the shapes grow or shrink?
What parts can we compare?
How can we write the comparison?
December 9, 2011 due December 12, 2011
4.3.3 (4-98 to 4-102)
Working With Corresponding Sides
Sometimes graphic artists have a shape that they need to make larger to use for a sign or make smaller to use for a bumper sticker. They have to be sure that the shapes look the same no matter what size they are. How do artists know what the side length of a similar shape should be, if it needs to be larger or smaller than the original?
December 12, 2011 due December 13, 2011
4.3.3 (4-108 to 4-112)
Solving Problems Involving Similar Shapes
Architects create scaled plans for building houses, artists use sketches to plan murals for the sides of buildings, and companies create smaller sizes of their products for display in stores. Each of these models is created to show all of the information about the “real” object, without being the actual size of the object. Today you will work with your team to find strategies that you can use when you are missing some of the information about a set of similar shapes. As you work, look for more than one way to solve the problem.
December 13, 2011
Chapter 3 Closure
Reflection and Synthesis
The activities below offer you a chance to reflect on
what you have learned during this chapter. As you
work, look for concepts that you feel very comfortable
with, ideas that you would like to learn more about, and
topics you need more help with. Look for connections
between ideas as well as connections with material you
learned previously.
Test
October 28, 2011
November 21, 2011
December 14, 2011
Assignments
October 31, 2011 due November 1, 2011
3.1.1 (3-7 to 3-11)
Area of Rectangular Shapes
Mathematics can be used to describe patterns in the world. Scientists use math to describe various aspects of life, including how cells multiply, how objects move through space, and how chemicals react. Often, when scientists try to describe these patterns, they need to describe something that changes or varies. Scientists call those quantities that change variables, and represent them using letters and symbols.
In this course you will spend time learning about variables, what they can represent, and how they can serve different purposes. To start, you will use variables to describe the dimensions and area of different shapes and begin to organize those descriptions into algebraic expressions.
As you work with your teammates, use the following questions to help focus your team’s discussion:
How can we organize groups of things?
What is the area?
Which lengths can vary?
November 1, 2011 due November 3, 2011
3.1.2 (3-18 to 3-23)
Naming Perimeters of Algebra Tiles
How much homework do you have each night? Some nights you may have a lot, while other nights you may have no homework at all. The amount of homework you have varies from day to day. In mathematics we use letters such as x and y, called variables, to represent quantities that are not constant.
In Lesson 3.1.1 you used variables to name lengths that could not be precisely measured. Using variables allows you to work with lengths that you do not know exactly. Today you will work with your team to write expressions to represent the perimeters of different shapes using variables. As you work with your teammates, use the following questions to help focus your team’s discussion:
Which lengths can vary?
How can we see the perimeter?
How can we organize groups of things?
Chapter 3 assignments to download
November 1, 2011 due November 3, 2011
3.1.1 (3-7 to 3-11)
Area of Rectangular Shapes
Mathematics can be used to describe patterns in the world. Scientists use math to describe
various aspects of life, including how cells multiply, how objects move through space, and
how chemicals react. Often, when scientists try to describe these patterns, they need to
describe something that changes or varies. Scientists call those quantities that change
variables, and represent them using letters and symbols.
In this course you will spend time learning about variables, what they can represent, and
how they can serve different purposes. To start, you will use variables to describe the
dimensions and area of different shapes and begin to organize those descriptions into
algebraic expressions.
As you work with your teammates, use the following questions to help focus your team’s
discussion:
How can we organize groups of things?
What is the area?
Which lengths can vary?
November 3, 2011 due November 4, 2011
3.1.2 (3-18 to 3-23)
Naming Perimeters of Algebra Tiles
How much homework do you have each night? Some nights you may have a lot, while
other nights you may have no homework at all. The amount of homework you have varies
from day to day. In mathematics we use letters such as x and y, called variables, to
represent quantities that are not constant.
In Lesson 3.1.1 you used variables to name lengths that could not be precisely measured.
Using variables allows you to work with lengths that you do not know exactly. Today you
will work with your team to write expressions to represent the perimeters of different
shapes using variables. As you work with your teammates, use the following questions to
help focus your team’s discussion:
Which lengths can vary?
How can we see the perimeter?
How can we organize groups of things?
November 4, 2011 due November 7, 2011
3.1.3 (3-29 to 3-33)
Combining Like Terms
In Lesson 3.1.2, you looked at different ways the perimeter of algebra tiles can be written,
and created different expressions to describe the same perimeter. Expressions that
represent the same perimeter in different ways are called equivalent. Today, you will
extend your work with writing and rewriting perimeters to more complex shapes. You
will rewrite expressions to determine whether two perimeters are equivalent or different.
As you work today, keep these questions in mind:
Are there like terms I can combine?
How can I rearrange it?
How can I see (visualize) it?
November 7, 2011 due November 8, 2011
3.1.4 (3-38 to 3-42)
Evaluating Variable Expressions
In the past three lessons, you have learned how to find the perimeter and area of a shape
using algebra tiles. Today, you will challenge the class to find the perimeter and area of
shapes that you create. As you work, keep in mind these questions:
Which lengths are constant?
Which lengths can change?
November 8, 2011 due November 10, 2011
3.1.5 (3-49 to 3-53)
Perimeter and Area of Algebra Tile Shapes
People often assume that area and perimeter are related. It seems reasonable that if the
area of a shape gets bigger (or smaller), then its perimeter should also get bigger (or
smaller). But is this always true? In Chapter 1 you learned that the “tiles” could stay the
same, but you could increase the “toothpicks” by changing the arrangement of squares. In
this lesson you will continue to investigate whether there is a relationship between
perimeter and area using algebra tiles.
As you work with your team, it is important that you share your ideas so that you are able
to understand many different ways of seeing the shapes. Be prepared to justify how you
are finding perimeters and how you are simplifying the expressions. Ask yourself these
questions to help you to explain your reasoning:
How can I see the perimeter?
Where am I adding (or covering) length?
How can I rearrange the tiles?
November 10, 2011 due November 11, 2011
3.2.1 (3-60 to 3-64)
Describing Relationships Between Quantities
You may not know it, but you use mathematical thinking every day. You think
mathematically when you figure out if you can afford items you want to buy, or when you
read a graph on a web page. You also think mathematically when you double a recipe or
when you estimate how much longer it will take to get somewhere based on how far you
still have to go. Math can describe many of the relationships in the world around you.
Building your interpretation skills and developing ways to represent situations will help
you solve problems. In this section you will learn new ways to show your thinking when
using math to solve problems. As you work today, think about the following questions:
How can I represent this with a diagram?
Who has more? Who has less?
November 11, 2011 due November 14, 2011
3.2.2 (3-71 to 3-75)
Solving a Word Problem
You have seen that being able to draw diagrams and describe relationships is helpful for
solving problems. In this lesson, you will learn another way to organize your thinking as
you solve word problems.
November 14, 2011 due November 15, 2011
3.2.3 (3-84 to 3-88)
Strategies for Using the 5-D Process
Math is used to solve challenging problems that apply to daily life. For example, how
much fresh water is on the planet? How many area codes (for telephone numbers) are
needed in a city? Where should a city build transportation lines such as city bus systems
and subways to reduce traffic on the freeways? Mathematics can provide helpful insights
for the solutions.
When trying to solve a new and challenging problem, it is useful to have a strategy. The
5-D Process that you learned about in Lesson 3.2.2 will often work when you are trying to
solve a problem you have not seen before.
In this lesson you will practice using this process to solve more word problems and you
will compare the different ways that your classmates use the 5-D Process to help them.
Be sure to write your work neatly and be prepared to justify your reasoning.
As you work using the 5-D Process, consider the following questions:
How can we describe the problem?
How can we decide how to label the columns?
How can we organize the columns?
How can we decide which quantity to start with?
Does it matter which one we choose?
How can we decide which number to try first?
November 15, 2011 due November 17, 2011
3.2.4 (3-99 to 3-103)
Using Variables to Represent Quantities in Word Problems
In Section 2.1, you used variables to help you describe the perimeter of tiles. In that
situation x could be stretched to represent any positive number. Today you will continue
to use the 5-D Process as you solve word problems and you will use a variable to represent
the unknown value in the problem.
Think of these questions as you work on the problems today:
What is the problem asking?
What is the relationship between the quantities involved?
How can I choose which part of the problem to represent with a variable?
November 17, 2011 due November 18, 2011
3.2.5 (3-105 to 3-108)
More Word Problem Solving
So far in Section 3.2, you have been using a 5-D Process as a way to organize and solve
problems. Today you will continue using this process to solve problems in a variety of
situations.
As you work, use the following questions to focus your team’s discussion:
What is the problem asking?
What is the relationship between the quantities involved?
How can we decide which part of the problem to represent as x ?
What if a different quantity were represented with x?
November 18, 2011
Chapter 3 Closure
Reflection and Synthesis
The activities below offer you a chance to reflect on
what you have learned during this chapter. As you
work, look for concepts that you feel very comfortable
with, ideas that you would like to learn more about, and
topics you need more help with. Look for connections
between ideas as well as connections with material you
learned previously.
October 7, 2011 due October 17, 2011
2.2.4 extension activity (2-85 to 2-89)
Using Rigid Transformations
In the last several lessons you have described translations using coordinates, and developed strategies for determining where an object started when you know how it was translated and its final position. In this lesson, you will continue to practice transforming objects on a coordinate grid by translating (sliding), rotating (turning), and reflecting (flipping). As you work, visualize what each object will look like after the transformation and use the graph to check your prediction.
October 17, 2011 due October 18, 2011
2.3.1 (2-97 to 2-101)
Multiplication of Fractions
You often only need part of something. You might need part of a gallon of gasoline to fill the tank of a scooter, part of a can of paint to finish covering a wall, or part of a piece of paper to complete an assignment.
But what happens when you need a part of a part? Cooks, construction workers, and city planners often need to find part of something that is already a part of something else.
As you work with your team to find parts of parts, be sure to draw diagrams and clearly label all of the pieces in them so that you know what they represent. Think about the following questions:
How can I represent it?
What does each part represent in the situation?
October 18, 2011 due October 20, 2011
2.3.2 (2-77 to 2-81)
Decomposing and Recomposing Area
In previous classes you have had experience with finding the area of squares and other rectangles, but what about finding the area of irregular shapes? Landscape designers, floor tilers, and others often have to deal with areas that are made of several shapes combined into one. As you work on the problems in this lesson, you will need to visualize the new shapes, and predict what they will look like after they are changed.
As you work through this section, it will be important to describe how you see different shapes and to organize your work to show your thinking. Ask each other these questions to get discussions started in your study team:
What other shapes can we see in this figure?
Where should we break this shape apart?
How should we rearrange the pieces?
Will the area change?
October 20, 2011 due October 21, 2011
2.3.3 (2-116 to 2-120)
Area of Parallelograms
In Lesson 2.3.2, you worked with your study team to rearrange two irregular shapes into rectangles in order to find their areas more easily. Today you will use a technology tool (available at www.cpm.org/students/technology) to investigate the question: Can all shapes be rearranged to make rectangles? As you work, visualize what each shape will look like cut into pieces and how those pieces could fit back together to make a rectangle. Ask yourself these questions while you investigate:
How can I break this shape apart?
How can I rearrange the pieces of the shape to make a new shape?
October 21, 2011 due October 24, 2011
2.3.4 (2-127 to 2-132)
Area of Triangles
So far in this chapter you found the area of different shapes by dividing them into smaller pieces and then putting the pieces back together to make rectangles. In this lesson you will look at strategies for making shapes larger in order to find their areas. As you work today, consider these questions:
How can I make a rectangle?
How are the areas related?
Which lengths help me find the area?
October 24, 2011 due October 25, 2011
2.3.5 (2-137 to 2-141)
Area of Trapezoids
In this chapter, you have used the process of cutting apart and rearranging shapes to help you find their areas. You have also made some shapes larger to help find their area. In this chapter you have developed several different strategies for finding the area of shapes. For example, you have found the sum of the areas of multiple smaller parts, rearranged smaller parts into rectangles to find area, and made shapes bigger in order to find their area. In this lesson you will focus on how to choose a strategy to find the area of a new shape: a trapezoid. As you work with your team, practice visualizing how each shape can be changed or rearranged. Ask each other these questions:
What strategy should we choose?
Which lengths are important?
October 25, 2011 due October 27, 2011
2.3.6 (2-151 to 2-155)
Order of Operations
If you know the length of the base and height of a triangle, how do you find its area? Some people reason this way: Since I know that two of the triangles can make a parallelogram, then the area of the triangle must be half the area of the parallelogram. Therefore, it is half the product of the length of the base and the length of the height.
However, this relationship can also be written as a rule, such as A = 1/2 bh, where A represents the area of theh triangle, b represents the length of the base, and h represents the height of the triangle.
There are many other relationships that can be written with symbols that you may have seen before. Perhaps one of the most famous rules is Einstein’s formula E = mc2 , relating energy, mass, and the speed of light. Work with your team to use some rules you already know to find a quantity.
October 27, 2011
Chapter 2 Closure - Answers are in the packet. Be ready for the test tomorrow.
Tests
November 18, 2011
Quarter 1
Assignments
October 3, 2011 due October 6, 2011
2.2.4 (2-77 to 2-81)
Multiplication and Dilation
When an object is translated, rotated or reflected, it stays the same size and shape even though it moves. For this reason, they are called rigid transformations. In this lesson you will explore a new transformation that changes how the object looks. As you work today, ask these questions in your team:
What parts of the shape are changing?
What parts stay the same?
What happens when we multiply by a negative number?
October 4, 2011
ISA testing. No class.
October 7, 2011 due October 17, 2011
2.2.4 extension activity (2-85 to 2-89)
Using Rigid Transformations
In the last several lessons you have described translations using coordinates, and developed strategies for determining where an object started when you know how it was translated and its final position. In this lesson, you will continue to practice transforming objects on a coordinate grid by translating (sliding), rotating (turning), and reflecting (flipping). As you work, visualize what each object will look like after the transformation and use the graph to check your prediction.
October 10-14
Break
October 17, 2011 due October 18, 2011
2.3.1 (2-97 to 2-101)
Multiplication of Fractions
You often only need part of something. You might need part of a gallon of gasoline to fill the tank of a scooter, part of a can of paint to finish covering a wall, or part of a piece of paper to complete an assignment.
But what happens when you need a part of a part? Cooks, construction workers, and city planners often need to find part of something that is already a part of something else.
As you work with your team to find parts of parts, be sure to draw diagrams and clearly label all of the pieces in them so that you know what they represent. Think about the following questions:
How can I represent it?
What does each part represent in the situation?
Tests
October 6, 2011
Test will cover coordinates (x,y) and quadrants. More practice can be found at these links:
Practice test
Coordinate teaching
Coordinate teaching 2